Proof: Collinear Angles Property 8
Let's prove the following theorem:
if m∠ABC = 180, then m∠XAB = m∠XAC
Proof:
Given
1 | m∠ABC = 180 |
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# | Claim | Reason |
---|---|---|
1 | m∠CBA = 180 | if m∠ABC = 180, then m∠CBA = 180 |
2 | m∠BAX = m∠CAX | if m∠CBA = 180, then m∠BAX = m∠CAX |
3 | m∠BAX = m∠XAB | m∠BAX = m∠XAB |
4 | m∠XAB = m∠CAX | if m∠BAX = m∠XAB and m∠BAX = m∠CAX, then m∠XAB = m∠CAX |
5 | m∠CAX = m∠XAC | m∠CAX = m∠XAC |
6 | m∠XAB = m∠XAC | if m∠XAB = m∠CAX and m∠CAX = m∠XAC, then m∠XAB = m∠XAC |
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